Beyond P values and Hypothesis Testing: Using the Minimum Bayes Factor to Teach Statistical Inference in Undergraduate Introductory Statistics Courses

While interest in Bayesian statistics has been growing in statistics education, the treatment of the topic is still inadequate in both textbooks and the classroom. Because so many fields of study lead to careers that involve a decision-making process requiring an understanding of Bayesian methods, it is becoming increasingly clear that Bayesian methods should be included in classes that cover the P value and Hypothesis Testing. We discuss several fallacies associated with the P value and Hypothesis Testing, including why Fisher’s P value and Neyman-Pearson’s Hypothesis Tests are incompatible with each other and cannot be combined to answer the question “What is the probability of the truth of one’s belief based on the evidence?” We go on to explain how the Minimum Bayes Factor can be used as an alternative to frequentist methods, and why the Bayesian approach results in more accurate, credible, and relevant test results when measuring the strength of the evidence. We conclude that educators must realize the importance of teaching the correct interpretation of Fisher’s P value and its alternative, the Bayesian approach, to students in an introductory statistics course.

[1]  Robert Rosenthal,et al.  Interpretation of significance levels and effect sizes by psychological researchers. , 1986 .

[2]  J. Lee,et al.  Demystify statistical significance--time to move on from the p value to bayesian analysis. , 2011, Journal of the National Cancer Institute.

[3]  R. L. Winkler,et al.  WHY BAYESIAN ANALYSIS HASN'T CAUGHT ON IN HEALTHCARE DECISION MAKING , 2001, International Journal of Technology Assessment in Health Care.

[4]  Gerd Gigerenzer,et al.  How to Improve Bayesian Reasoning Without Instruction: Frequency Formats , 1995 .

[5]  Rex B. Kline,et al.  Beyond Significance Testing: Reforming Data Analysis Methods in Behavioral Research , 2004 .

[6]  R. Kirk Elementary Statistics. 4th ed. , 1983 .

[7]  Z. Dienes Bayesian Versus Orthodox Statistics: Which Side Are You On? , 2011, Perspectives on psychological science : a journal of the Association for Psychological Science.

[8]  Allan G. Bluman Elementary Statistics: A Step By Step Approach , 1980 .

[9]  G. Gigerenzer Mindless statistics , 2004 .

[10]  D. Ashby Bayesian statistics in medicine: a 25 year review , 2006, Statistics in medicine.

[11]  S. Goodman Toward Evidence-Based Medical Statistics. 1: The P Value Fallacy , 1999, Annals of Internal Medicine.

[12]  E. S. Pearson,et al.  On the Problem of the Most Efficient Tests of Statistical Hypotheses , 1933 .

[13]  R. Fisher PROFESSOR KARL PEARSON AND THE METHOD OF MOMENTS , 1937 .

[14]  G. Gigerenzer,et al.  The null ritual : What you always wanted to know about significance testing but were afraid to ask , 2004 .

[15]  S. Goodman A dirty dozen: twelve p-value misconceptions. , 2008, Seminars in hematology.

[16]  S. Goodman Introduction to Bayesian methods I: measuring the strength of evidence , 2005, Clinical trials.

[17]  Sander Greenland,et al.  Living with P Values: Resurrecting a Bayesian Perspective on Frequentist Statistics , 2013, Epidemiology.

[18]  R. Matthews,et al.  Why should clinicians care about Bayesian methods , 2001 .

[19]  David S. Moore,et al.  Undergraduate Programs and the Future of Academic Statistics , 2001 .

[20]  E. Satake,et al.  Teaching an Application of Bayes' Rule for Legal Decision-Making: Measuring the Strength of Evidence , 2014 .

[21]  R. Serlin,et al.  Misuse of statistical test in three decades of psychotherapy research. , 1994, Journal of consulting and clinical psychology.

[22]  Eiki Satake,et al.  An Alternative Version of Conditional Probabilities and Bayes' Rule: An Application of Probability Logic. , 2008 .

[23]  Bruce Thompson,et al.  A National Survey of AERA Members' Perceptions of Statistical Significance Tests and Other Statistical Issues. , 2000 .

[24]  P. Pollard,et al.  On the probability of making Type I errors. , 1987 .

[25]  Steven Goodman Toward Evidence-Based Medical Statistics. 2: The Bayes Factor , 1999, Annals of Internal Medicine.

[26]  H. Katki Invited Commentary Invited Commentary: Evidence-based Evaluation of p Values and Bayes Factors , 2008 .

[27]  W. M. Bolstad TEACHING BAYESIAN STATISTICS TO UNDERGRADUATES: WHO, WHAT, WHERE, WHEN, WHY, AND HOW ® , 2002 .

[28]  Robert M. Capraro,et al.  Treatments of Effect Sizes and Statistical Significance Tests in Textbooks , 2002 .

[29]  Sabine Schulze,et al.  Statistics A Bayesian Perspective , 2016 .

[30]  Judith L. Anderson Embracing Uncertainty: The Interface of Bayesian Statistics and Cognitive Psychology , 1998 .